In his work on
set theory
Set theory is the branch of mathematical logic that studies Set (mathematics), sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathema ...
,
Georg Cantor
Georg Ferdinand Ludwig Philipp Cantor ( ; ; – 6 January 1918) was a mathematician who played a pivotal role in the creation of set theory, which has become a foundations of mathematics, fundamental theory in mathematics. Cantor establi ...
denoted the collection of all
cardinal number
In mathematics, a cardinal number, or cardinal for short, is what is commonly called the number of elements of a set. In the case of a finite set, its cardinal number, or cardinality is therefore a natural number. For dealing with the cas ...
s by the last letter of the
Hebrew alphabet
The Hebrew alphabet (, ), known variously by scholars as the Ktav Ashuri, Jewish script, square script and block script, is a unicase, unicameral abjad script used in the writing of the Hebrew language and other Jewish languages, most notably ...
, (transliterated as Tav, Taw, or Sav.) As Cantor realized, this collection could not itself have a cardinality, as this would lead to a paradox of the
Burali-Forti type. Cantor instead said that it was an "inconsistent" collection which was
absolutely infinite.
The Correspondence between Georg Cantor and Philip Jourdain
I. Grattan-Guinness, ''Jahresbericht der Deutschen Mathematiker-Vereinigung'' 73 (1971/72), pp. 111–130, at pp. 116–117.
See also
* Taw
Taw, tav, or taf is the twenty-second and last letter of the Semitic abjads, including Arabic ''tāʾ'' , Aramaic ''taw'' 𐡕, Hebrew ''tav'' , Phoenician ''tāw'' 𐤕, and Syriac ''taw'' ܬ. In Arabic, it also gives rise to the derived ...
* Aleph number
In mathematics, particularly in set theory, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets. They were introduced by the mathematician Georg Cantor and are named after the symbol he used t ...
* Absolute infinite
References
Cardinal numbers
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